The next important step was done in the seminal paper [1]}
by Fradkin and Tseytlin. This was the first publication were the
relevance of the weight operator (REF ) for quantum
contributions was noted, there was also the first heat-kernel
treatment of the fourth derivative operator and of the non-minimal
vector operator, the first discussion of the IR decoupling in higher
derivative theories, and the first observation concerning the
difference between general and conformal QG models. We can say,
that [1]} paved the way for the development of a large part
of QG in the subsequent decades. Furthermore, the correct result
for the general and conformal versions of the fourth-derivative QG
models was obtained in [3]} and [4]}, respectively.
Finally, there was a confirmation of the correctness of these results
in [5]}, [6]}, where another interesting aspect of QG was
addressed. Much earlier, in the paper [7]}, it was noted
that the Gauss-Bonnet term \(\int E_4\)  may play a nontrivial role in
QG. The point is that the topological nature of this term becomes
badly seen in the perturbative approach, especially if one uses the
dimensional regularization. In the previous sections we saw that the
topological term does not contribute to the propagator, in any
dimension \(n\) . However, for \(n \ne 4\)  it does affect the vertices.
The question posed in [7]} was whether it is true that the
contributions of these vertices cancel in the divergent part of
effective action, or even in the finite part of it. The answer is that
the divergences really do not depend on the \(\int E_4\)  term, and
this dependence takes place only in the local finite terms.
